Question

​a) Using the SPT​ (shortest processing​ time) decision rule for sequencing the​ jobs, the order is​ (to resolve a​ tie, use the order in which the jobs were​ received): Sequence Job 1 ▼ N L M K O 2 ▼ K O L M N 3 ▼ K N L O M 4 ▼ N L M O K 5 ▼ N O K M L The total flow time for the sequence developed using the SPT rule​ = nothing days ​(round your response to two decimal​ places). The percentage utilization for the sequence developed using the SPT rule​ = nothing​% ​(enter your response as a percentage rounded to two decimal​ places). The average number of jobs in the system for the sequence developed using the SPT rule​ = nothing jobs ​(round your response to two decimal​ places). The average tardiness​ (job lateness) for the sequence developed using the SPT rule​ = nothing days ​(round your response to two decimal​ places). ​b) Using the LPT​ (longest processing​ time) decision rule for sequencing the​ jobs, the order is​ (to resolve a​ tie, use the order in which the jobs were​ received): Sequence Job 1 ▼ L N K M O 2 ▼ N M K L O 3 ▼ L O M N K 4 ▼ K L O N M 5 ▼ O M L N K The total flow time for the sequence developed using the LPT rule​ = nothing days ​(round your response to two decimal​ places). The percentage utilization for the sequence developed using the LPT rule​ = nothing​% ​(enter your response as a percentage rounded to two decimal​ places). The average number of jobs in the system for the sequence developed using the LPT rule​ = nothing jobs ​(round your response to two decimal​ places). The average tardiness​ (job lateness) for the sequence developed using the LPT rule​ = nothing days ​(round your response to two decimal​ places). At​ ADM's maintenance​ facility, following jobs​ (below) are ready for dispatching to a machine center. The processing​ times, date job​ received, and due dates for the jobs are given below. In what sequence would the jobs be ranked according to the decision rules on the left. The jobs are to be scheduled​ today, which is day 239 in​ ADM's manufacturing planning calendar days. Compute all times based on initiating​ (starting) work on day 239.                                                                            Job Date Job Received Due Date Processing​ (days) Upper K 230 320 35 Upper L 235 360 40 Upper M 231 310 30 Upper N 228 300 15 Upper O 225 270 25 Enter your answer in each of the answer boxes.

Answer 1

Initiating Work Day 239 a) First Come First Served (FCFS) priority rule Jobs are scheduled in order of their arrival Due Duration Release Total Time Date job received date Completion Time (days)Time (Ri) (Ci-MAX(Ri,Ci-1) + Pi) (Fi= Cl-Ri)| (Si = Ci-Ji+1 ) Flow Time Tardiness Sequence in System Job Ti Max(0,Ci-Di) (Ji) (Di) (Pi) 225 270 25 239 263 25 39 40 2 228 300 15 239 278 51 C 3 K. 230 320 35 239 313 75 84 4 M 231 310 30 239 343 105 113 33 5 235 360 40 239 383 145 149 23 Σ= 145 1580 390 436 56 Makespan Pi 145.00 = Total Flow Time - 2Fi 390.00 Percentage Utilisation Average Number of Jobs in System= 2Fi/2Pi Average Tardiness = Ti/n, where n-5 ΣΡi/ΣFi 37.18% 2.69 11,20 Initiating Work Day 239 b) Earliest Due Date (EDD) priority rule Jobs are scheduled in increasing order of their due date Date job received Duration Total Time Due Release Flow Time Tardiness Completion Time Sequence (days)Time (Ri) (Ci-MAX(Ri,Ci-1) + Pi) (FI=CHRO)(Si- Ci-Ji+1) (Pi) Job date in System Ti Max(0,Ci-Di) (Ji) (Di) 1 225 270 25 239 263 25 39 0 40 2 N 228 300 15 239 278 51 M 231 310 30 239 308 70 78 4 K 230 320 35 239 343 105 114 23 5 L 235 360 40 239 383 145 149 23 Σ= 145 1575 385 431 46 Makespan EPi Total Flow Time Fi Percentage Utilisation EPi/Fi Average Number of Jobs in System= 2Fi/2Pi Average Tardiness Ti/n, where n=5 145,00 385.00 37.66% 2.66 9.20

Initiating Work Day 239 c) Shortest Processing Time (SPT) priority rule Jobs are scheduled in increasing order of their processing time Date job Due Duration Release Total Time Completion Time (days)Time (Ri) (Ci-MAX(Ri,Ci-1) + Pi) | (Fi = CI-Ri) Flow Time Tardiness Sequence received date in System (Si = Ci-Ji+1) Job Ti Max(0,Ci-Di) (Ji) (Di) (Pi) 1 N 228 300 15 239 253 15 26 2 O 225 270 25 239 278 40 54 70 3 M 231 310 30 239 308 78 4 K. 230 320 35 239 343 105 114 23 5 235 360 40 239 383 145 149 23 Σ= 145 1565 375 421 54 Makespan EPi Total Flow Time EFi 145.00 375.00 Percentage Utilisation Average Number of Jobs in System - Fi/Pi |Average Tardiness = ETi/n, where n=5 ΣΡi/ΣFi 38.67% 2.59 10.80 Initiating Work Day 239 d) Longest Processing Time (LPT) priority rule Jobs are scheduled in decreasing order of their processing time Due Duration Release Date job received Total Time Completion Time (days)Time (Ri) (Ci-MAX(Ri,Ci-1) + Pi) (Fi= Ci-RI)(Si = Ci-Ji+1) Tardiness Ti= Max(0,Ci-Di) Flow Time Sequence in System Job date (Di) (Ji) (Pi) 40 1 235 360 40 239 278 44 0 2 K 230 320 35 239 313 75 84 3 M 231 310 30 239 343 105 113 33 4. C 225 270 25 239 368 130 144 98 5 N 228 300 15 239 383 145 156 83 145 1685 495 541 214 Makespan EPi Total Flow Time Fi 145.00 495.00 - Percentage Utilisation EPi/Fi Average Number of Jobs in System Fi/Pi Average Tardiness ETi/n, where n-5 29.29% 3.41 42.80